Deployed in various distributed storage systems, erasure coding has demonstrated its advantages of low storage overhead and high failure tolerance. Typically in an erasurecoded distributed storage system, systematic maximum distance seperable (MDS) codes are chosen since the optimal storage overhead can be achieved and meanwhile data can be read directly without decoding operations. However, data parallelism of existing MDS codes is limited, because we can only read data from some specific servers in parallel without decoding operations. In this paper, we propose Carousel codes, designed to allow data to be read from an arbitrary number of servers in parallel without decoding, while preserving the optimal storage overhead of MDS codes. Furthermore, Carousel codes can achieve the optimal network traffic to reconstruct an unavailable block. We have implemented a prototype of Carousel codes on Apache Hadoop. Our experimental results have demonstrated that Carousel codes can make MapReduce jobs finish with almost 50% less time and reduce data access latency significantly, with a comparable throughput in the encoding and decoding operations and no additional sacrifice of failure tolerance or the network overhead to reconstruct unavailable data.